ON  THE  VISCOSITY  OF  CERTAIN  SALT  SOLUTIONS. 


By  B.  E.  Moore. 


HE  subject  of 'Viscosity  was  first  taken  up  by  Poiseuille,1 


-L  who  used  a method  depending  upon  the  transpiration  of  the 
liquid  through  capillary  tubes.  Coulomb,*  in  studying  the  same 
subject,  observed  the  damping  of  a magnetic  needle  or  bar  when 
vibrating  in  the  liquid  investigated.  - This  method  was  also  exten- 
sively used  by  O.  E.  Meyer,2  Grotian,3  and  others.  Still  a third 
method  has  been  developed  by  Helmholtz,  who  placed  the  solution 
to  be  studied  in  a hollow  sphere,  and  observed  the  behavior  of  the 
sphere  when  oscillated. 

These  methods  have  led  to  very  different  results.  Konig4 
modified  the  method  of  Coulomb  and  used  in  the  place  of  the 
swinging  rod,  a sphere,  the  equation  of  motion  of  which  Kirchhoff 
had  solved,  and  for  which  the  theory  can  be  completely  developed. 
For  calculation  Konig  made  use  of  the  expression  by  Kirchhoff  as 
extended  and  completed  by  Boltzman,  and  reached  the  conclusion 
that  the  values  obtained  for  viscosity  by  Coulomb’s  method  were 
in  complete  agreement  with  the  results  obtained  by  allowing  the 
liquid  to  flow  through  a capillary  tube.  Though  the  agreement 

1 Memoirs  des  Savants  Etrangers,  T.  IX.  Pogg.  Ann.,  Vol.  LVIII.,  p.  434. 

2Pogg.  Ann.,  Vol.  CXIII.,  pp.  55,  193,  383.  3 Pogg.  Ann.,  Vol.  CLVII.,  p.  130. 

4 Wied.  Ann.,  Vol.  XXXII.,  p.  193. 


321 


322 


B.  E.  MOORE. 


[Vol.  III. 


of  results  by  the  different  methods  is  of  great  interest  and 
importance,  yet  observers  have  generally  preferred  the  original 
method  due  to  Poiseuille,  and  that  because  of  its  simplicity. 
The  method  requires  also  a considerably  smaller  amount  of  the 
solution,  and  admits  of  a much  easier  and  more  accurate  tempera- 
ture regulation. 

Among  the  earlier  investigations  on  the  subject  of  viscosity 
may  be  mentioned  those  of  Graham,1  whose  results  suggest  the 
presence  of  hydrates  in  solution.  He  states  further  that  “slow 
transpiration  and  low  volatility  go  together.”  Later  investi- 
gations by  Rellstab2  dealt  with  several  organic  liquids,  while 
numerous  experiments  were  made  by  Hiibner3  on  the  salts  of  the 
chloride  family.  Sprung4  investigated  a great  many  cases  of 
varying  concentration  and  temperature,  the  latter  ranging  from 
o°  to  6o°  C. 

Hagenbach5  developed  the  mathematical  formula  for  transpira- 
tion. His  expression  for  viscosity  (rj)  reduces,  when  correction 
for  the  velocity  of  flow  is  omitted,  to  the  form  known  as  Poi- 

seuille’s  formula:  v = — 1 ^lst  ■ Herein  r denotes  the  radius  of  the 
8 Iv 

capillary ; h , the  height  of  pressure  column  ; j,  specific  gravity,  and 
therefore  the  product  of  h and  ^ the  pressure ; v represents  the 
volume  that  transpires  in  time,  t\  and  l is  used  to  designate 
the  length  of  the  capillary  tube. 

Pribam  and  Handl6  have  made  extensive  observations  on  the 
viscosity  of  organic  solution  and  stochiometrical  relations  of  the 
same.  The  careful  work  of  Gartenmeister 7 in  this  field  should 
not  be  omitted.  Grotian8  was  the  first  to  make  extended  com- 
parisons of  viscosity  and  conductivity  of  salt  solutions.  Slotte’s  9 
investigations  cover  a number  of  chromates  and  he  shows  that  the 
temperature  variation  in  viscosity,  77,  can  be  expressed  by  a for- 
mula, 7}  = c(  1 + bt)n , where  c,  b , and  n are  constants  of  the  liquid. 

1 Royal  Society  Proceedings,  XI.,  p.  381.  i860. 

2 Inaugural  Dissertation,  Bonn,  1868.  5Pogg.  Ann.,  Vol.  CIX.,  p.  385. 

3 Pogg.  Ann.  Vol.  CL.,  p.  248.  6 Wien  Ber.,  Vols.  78,  80. 

4 Pogg.  Ann.,  Vol.  CLIX.,  p.  1.  7Zeitschrift  die  Ph.  Chem.,  Vol.  VI.,  p.  524. 

8 Pogg.  Ann.,  Vol.  CLVII,  p.  130;  Vol.  CLX. , p.  238.  Wied.  Ann.,  Vol.  VIII., 

p.  530.  9 Wied.  Ann.,  Vol.  XIV.,  p.  13. 


No.  5.] 


VISCOSITY  OF  SALT  SOLUTIONS. 


323 


Since  the  announcement  of  the  dissociation  theory  by  Arrhenius, 
the  subject  of  viscosity  of  solutions  has  had  a much  deeper  interest, 
and  experiments  have  been  carried  on,  both  trying  to  establish 
some  stochiometrical  relation,  and  to  establish  a relation  between 
viscosity  and  conductivity.  With  this  idea  in  view,  Arrhenius  has 
made  many  investigations.  In  his  first  experiments 1 he  shows 
that  the  viscosity  is  a function  of  x and  y}  or  H (x,  y),  where  x 
and  y express  either  percentage  of  substance  in  solution,  or  gram- 
equivalent  per  liter.  We  may  say  rj  = H(x,  y)=AxBy,  where  A and 
B are  constants  of  the  solution.  For  a single  salt  in  solution  this 
reduces  to  rj  = Ax.  Wagner2  and  Reyher3  validified  this  law  for  a 
great  many  solutions.  In  Gartenmeister’s4  experiments  the  Arrhe- 
nius exponential  formula  is  not  so  well  satisfied.  Reyher  found 
a characteristic  relation  between  the  friction  or  viscosity  of  free 
acids  and  those  of  the  sodium  salts,  according  as  a strong  or  weak 
acid  was  present.  This  variation  he  made  to  depend  upon  the 
unequal  dissociation  of  the  strong  and  weak  acids.  The  dissociation 
theory  has  given  great  confidence  to  the  belief  in  a relation  of 
viscosity  to  conductivity.  However,  G.  Wiedemann,5  previous  to 
this  theory,  noticed  that  the  friction  which  the  ions  undergo 
varies  in  the  same  way  as  inner  friction ; i.e.  viscosity.  The 
mobility  of  the  ions  must  then  be  a function  of  their  fluidity. 
Arrhenius  showed  that  conductivity  did  not  depend  upon  fluidity 
alone.  This  investigator  made  a strong  point  when  he  showed 
that  the  introduction  of  a non-conducting  substance  into  an  elec- 
trolyte affected  both  its  conductivity  and  its  viscosity  in  the  same 
way.6  Other  experimenters,  by  a direct  comparison  of  conductiv- 
ities and  viscosities,  have  come  to  the  conclusion  that  while  the 
conductivities  of  a series  of  salts  increased,  the  viscosities  in  gen- 
eral decreased.  However,  the  increasing  and  decreasing  series 
stand  in  no  definite  ratio  to  each  other. 

The  following  experiments  have  followed  much  in  the  same  line. 

1Zeitschrift  die  Ph.  Chem.,  Vol.  I.,  p.  285. 

2 Zeitschrift  die  Ph.  Chem.,  Vol.  V.,  p.  31. 

3 Zeitschrift  die  Ph.  Chem.,  Vol.  II.,  p.  744. 

% 4 Zeitschrift  die  Ph.  Chem.,  Vol.  VI.,  p.  524. 

5 Pogg.  Ann.,  Vol.  XCIX.,  p.  177. 

6 Zeitschrift  die  Ph.  Chem.,  Vol.  IX.,  p.  487. 


3H 


• # 

B.  E.  MOORE.  [Vol.  III. 

The  viscosities  of  a series  of  salts  have  been  determined,  and,  in 
so  far  as  was  possible,  the  conductivities  of  the  same  compared 
with  their  viscosities. 

The  method  employed  was  the  one  due  to  Poiseuille,  the 
apparatus  being  similar  to  that  used  by  Arrhenius.  A glass  vessel 
A (Fig.  i),  of  about  24  c.cm.  capacity,  is  connected  with  two  tubes, 
a and  b,  above  and  below  respectively.  Each  tube  has  a diameter 
of  about  4 mm.  A stopcock  closes  a about  4 cm.  from  A.  b was 
joined  to  a capillary  tube  d , some  40  cm.  long.  The  lower  end  of 
the  capillary  dips  into  the  solution  to  be  studied,  contained  in  a 
glass  vessel,  B,  of  about  200  c.cm.  capacity.  B is  kept  water- 
tight by  means  of  a rubber  cork  e>  and  is  encased 
in  a brass  support  h.  Exactly  50  c.cm.  of  the  solu- 
tion was  always  brought  into  the  vessel  B,  and  the 
extremity  c of  the  capillary  brought  into  the  plane  of 
the  upper  edge  of  the  brass  casing  h.  This  was  done 
to  secure  a constant  average  height  of  pressure  in  all 
cases.  But  this  was  later  proven  to  be  an  unneces- 
sary precaution,  as  a change  in  the  length  of  the  capil- 
lary, amounting  to  18  cm.,  only  made  a difference  of 
2.5  seconds  in  the  transpiration  of  water  at  i8°C. 
The  liquid  is  brought  into  the  vessel  A to  some 
point  a ' by  exhausting  the  air  through  a rubber  tube 

Lg — qJ 'v  f.  The  time  of  flow  was  taken  between  two  marks 

Fig  j on  tubes  a and  b.  As  the  mean  height  of  the  pressure 
column  is  constant,  it  is  evident  that  the  pressure 
of  the  different  liquids  subjected  to  transpiration  varies  directly 
as  their  specific  gravities.  So  that  to  obtain  the  transpiration  at 
constant  pressure,  it  was  only  necessary  to  multiply  the  observed 
time  of  flow  by  the  specific  gravity  of  the  solution.  The  time  of 
flow  of  water  at  i8°C.  was  taken  as  standard.  The  ratio  of  the 
•corrected  time  of  flow  of  a solution  to  that  of  water  gives  the 
relative  viscosity  in  terms  of  water  as  unity.  Should  the  absolute 
viscosity  be  desired,  it  is  only  necessary  to  multiply  this  result  by 
the  absolute  value  of  water.  Relative  values  only  have  been 
calculated,  as  the  object  was  to  make  a comparison  of  solutions. 
The  temperature  was  regulated  by  a water-bath,  and  two  ther- 


No,  5.] 


VISCOSITY  OF  SALT  SOLUTIONS. 


325 


mometers  enabled  one  to  note  the  temperature  to  tenths  of 
a degree.  Hagenbach’s  correction  for  velocity  of  transpiration 
was  sufficiently  small  to  neglect  in  all  cases. 

The  specific  gravities  of  the  solutions  were  determined  by 
means  of  a calibrated  Mohr’s  balance,  which  enabled  one  to  take 
readings  to  the  fourth  decimal  place.  It  was  part  of  the  original 
intention  to  make  the  solutions  from  -Weighed  portions  of  the 
salts  and  of  fixed  molecular  (eg.  double  normal,  normal,  half 
normal,  etc.)  contents,  but  the  discovery  of  a mistake  in  the 
weight  of  a crucible  made  it  necessary  to  interpret  in  many  cases 
the  per  cent  of  salt  in  solution  from  tables  of  percentages  and 
specific  gravities.  Solutions  of  K2C03,  KOH,  NaOH,  and  K2S04 
were  made  from  Kohlrausch’s  tables.1  Solutions  of  Na2C03, 
KHC03,  NaHC03,  KHS04  Na2HP04,  NaH2P04,  K2C204  and 
NaHC4H4Oe  were  made  fr.om  carefully  weighed  quantities  of  the 
silts.  Solutions  of  K3P04,  K2HP04,  KH2P04  were  kindly  loaned 
by  Herr  Forch.  All  other  solutions  were  made  from  Landolt  and 
Bernstein’s  Tabellen  (2 te  Atiflage).  The  specific  gravities  of  solu- 
tions of  Na2C03  check  well  with  Kohlrausch’s  tables,  but  not  so 
well  with  those  of  Landolt  and  Bernstein.  The  specific  gravities 
of  Na2HP04  differ  also  slightly  from  the  latter  tables  and  in  solu- 
tions of  K2C204  the  difference  is  quite  large.  However,  specific 
gravities  of  K2C204  interpolated  from  Landolt  and  Bernstein’s 
Tabellen  give  a viscosity  curve  of  doubtful  character. 

The  time  of  flow  was  noted  over  considerable  range  of  tempera- 
ture from  which  the  time  transpiration  at  180  was  graphically  inter- 
polated. By  repeated  observation  the  error  in  time  is  reduced  to 
about  0.3  seconds.  In  the  following  table  of  observations  and 
results,  m denotes  the  gram-molecular  contents  ; j,  the  specific 
gravity ; T,  the  time ; and  77,  the  calculated  viscosities.  In  the 
rows  containing  neither  T nor  j,  the  values  of  m and  77  have 
been  graphically  interpolated. 

1 Kohlrausch : Leitfaden  der  practical  Physik,  7te  Auflage. 


326 


B.  E.  MOORE. 


[VOL.  III. 


Table  I. 


Na2C03 

NaHCOg 

m 

T 

V 

m 

T 

•>7 

0 00 

0.9987 

197.0 

1.000 

0.00 

0.9987 

194.5 

1.000 

0.25 

1.0250 

220.6 

1.120 

0.25 

1.0139 

205.5 

1.057 

0.5 

1.0517 

251.0 

1.274 

0.5 

1.0286 

218.0 

1.121 

1.0 

1.0980 

328.5 

1.667 

1.0 

1.0575 

245.0 

1.260 

2.0 

1.1880 

616.2 

3.128 

k2co3 

KHCOs 

0.00 

0.9987 

197.0 

1.000 

0.00 

0.9987 

194.5 

1.000 

0.25 

— 

— 

1.059 

0.25 

1.0146 

200.5 

1.031 

0.273 

1.0340 

210.0 

1.066 

0.495 

1.0298 

206.5 

1.062 

0.4788 

1.0577 

223.0 

1.132 

0.5 

— 

— 

1.065 

0.5 

— 

— 

1.138 

1.0 

1.0581 

218.0 

1.121 

0.9456 

1.1100 

258.0 

1.310 

1.98 

1.1149 

250.0 

1.285 

1.0 

— 

— 

1.341 

2.0 

— 

— 

1.290 

1.974 

1.2183 

381.0 

1.934 

2.0 

— 

— 

1.950 

Table  II. 


NaHS04 

NaOH 

m 

T 

V 

m 

1 T 

V 

0.00 

0.9987 

194.5 

1.0000 

0.00 

0.9987 

194.5 

1.0000 

0.25 

1.0186 

206.0 

1.059 

0.25 

1.0099 

206.0 

1.059 

0.5 

1.0386 

214.0 

1.100 

0.5 

1.0212 

215.5 

1.108 

1.0 

1.0753 

245.0 

1.260 

1.0 

1.0425 

240.0 

1.234 

2.0 

1.1475 

315.5 

1.622 

2.0 

1.0843 

299.0 

1.537 

4.0 

1.2810 

559  0 

2.874 

4.0 

1.1551 

552.0 

2.837 

k,so4 

8.0 

1.2786 

1470.0 

7.557 

0.00 

0.9987 

194.5 

1.000 

KOH 

0.1195 

1.0165 

198.1 

1.019 

0.00 

0.9987 

194.5 

1.0000 

0.125 

— 

— 

— 

0.25 

— 

— 

1.025 

0.243 

1.0328 

204.5 

1.051 

0 456 

1.0212 

203.0 

1.044 

0.25 

— 

— 

1.052 

0.5 

— 

— 

■1.051 

0.49 

1 .0650 

214.0 

1.100 

0.92 

1.0433 

213.5 

1.098 

0.50 

— 

— 

1.106 

1.00 

— 

— 

1.110 

KHSOd 

1.82 

1.0864 

235.5 

1.211 

2.0 





1.237 

0.00 

0.9987 

194.5 

1.0000 

4.0 

1.1793 

307.0 

1.578 

0.5 

1.0439 

209.5 

1.075 

6.8 

1.2900 

452.0 

2.324 

1.0 

1.0866 

223.5 

1.149 

2.0 

1.1712 

263.0 

1.352 

No.  5.] 


VISCOSITY  OF  SALT  SOLUTIONS. 


327 


Table  III. 


NaoHPOj 


m 

$ 

T 

V 

m 

T 

V 

0.00 

0.9987 

194.5 

1.000 

0.00 

0.9987 

194.5 

1.000 

0.125 

1.0190 

211.3 

1.086 

0.125 

— 

— 

1.098 

0.25 

1.0366 

231.4 

1.189 

0.14 

1.0222 

214.9 

1.105 

0.5 

1.0741 

277.5 

1.427 

0.25 

— 

— 

1.220 

0.276 

1.0440 

242.3 

1.246 

0.50 





1.504 

NaH2P04 

0.54 

1.0860 

367.2 

1.579 

0.00 

0.9987 

194.5 

1.000 

0.25 

1.0184 

209.3 

1.076 

^3ru4 

0.5005 

1.0391 

230.0 

1.182 

1.001 

1.0776 

274.0 

1.409 

0.00 

0.9987 

194.5 

1.000 

2.002 

1.1677 

450.0 

2.313 

0.125 

1.0227 

208.5 

1.070 

0.25 

1.0471 

219.0 

1.126 

KH,PO, 

0.5 

1.0933 

252.5 

1.298 

1.0 

1.1805 

342.2 

1.759 

0.00 

0.9987 

194.5 

1.000 

0.25 

1.0220 

205.5 

1.057 

rw2nru4 

0.5 

1.0442 

223.0 

1.146 

1.0 

1.0885 

254.0 

1.306 

0.00 

0.9987 

194.5 

1.000 

0.125 

1.0167 

202.0 

1.039 

T t nn 

0.25 

1.0343 

213.0 

1.095 

0.5 

1.0700 

234.0 

1.206 

1.0 

1 ; 1383 

300.0 

1.542 

0.00 

0.9987 

194.5 

1.000 

2.0 

1.2633 

449.0 

2.309 

0.25 

1.0120 

207.0 

1.064 

0.5 

1.0251 

222.3 

1.143 

1.0 

1.0508 

255.0 

1.311 

2.0 

1.1022 

338.3 

1.739 

Na3P04 


328 


B.  E.  MOORE . 


[VOL.  III. 


Table  IV. 


N &2C4H4O6 

NaKC4H4Oe 

m 

$ 

T 

V 

m 

T 

V 

0.00 

0.9987 

194.5 

1.000 

0.00 

0.9987 

194.5 

1.000 

0.141 

1.0185 

209.0 

1.075 

0.20 

1.0273 

212.5 

1.092 

0.25 

f 

— 

1.148 

0.25 

— 

— 

1.112 

0.281 

1.0368 

226.0 

1.162 

0.40 

1.05(7 

231.0 

1.188 

0.5 

— 

— 

1.335 

0.50 

— 

— 

1.252 

0.562 

1.0730 

269.0 

1.383 

0.789 

1.1087 

287.0 

1.476 

1.0 

— 

— 

1.823 

1.0 

— 

— 

1.679 

1.121 

1.1427 

395.0 

2.031 

1.656 

1.2112 

484.0 

2.488 

H2C4H4Oe 

k2c4h4o6 

0.00 

0.9987 

194.5 

1.000 

0.00 

0.9987 

194.5 

1.000 

0.233 

1.013 

207.5 

1.067 

0.1815 

1.0267 

205.5 

1.057 

0.25 

— 

— 

— 

0.25 

— 

— 

1.080 

0.467 

1 .0269 

221.5 

1.139 

0.363 

1.0525. 

220.0 

1.131 

0.5 

— 

— 

1.160 

0.5 

— 

— 

1.195 

0.833 

1.0542 

256.0 

1.316 

0.7345 

1.1036 

255.0 

1.342 

1.0 

— 

— 

1.412 

1.0 

— 

— 

1.489 

1.478 

— 

330.0 

1.696 

1.48 

1.2072 

363.0 

1.866 

1.666 

1.1092 

365.0 

1.853 

1.5 

— 

— 

(1.883) 

c4hgo4 

k2c2o4 

0.00 

0.9987 

194.5 

1.000 

0.00 

0.9987 

194.5 

1.000 

0.242 

1.0076 

204.2 

1.050 

0.25 

1.0283 

204.0 

1.049 

0.25 

— 

— 

1.052 

0.5 

1.0571 

214.5 

1.103 

0.483 

1.0166 

215.0 

1.105 

1.0 

1.1121 

239.5 

1.232 

0.5 

— 

— 

(1.110) 

1.5 

1.1663 

270.2 

1.389 

H2C204 

NaHC4H406 

0.00 

0.9987 

194.5 

1.000 

0.00 

0.9987 

194.5 

1.000 

0.25 

— 

— 

1.045 

0.147 

1.0121 

205.5 

1.056 

0.326 

1.0116 

206.0 

1.059 

0.25 

— 

— 

1.094 

0.5 

— 

— 

1.072 

0.294 

1.0256 

217.0 

1.116 

0.665 

1.0300 

217.5 

1.118 

0.441 

1.0386 

228.5 

1.175 

0.848 

1.0370 

224.5 

1.154 

0.5 

— 

— 

(1.198) 

1.0 

— 

— 

(1.199) 

No.  5.] 


VISCOSITY  OF  SALT  SOLUTIONS. 


329 


Curves. 

The  curves  (Figs.  2,  3,  4,  and  5)  correspond  to  Tables  I.,  II., 
III.,  and  IV.  of  data  respectively.  The  curve  for  H2S04  (Fig.  3) 
is  drawn  from  data  by  Grotian  and  is  given  in  order  to  show 


0.25  0.50  0.75  1.  m.  1.25  1.50  1.75  2.m. 


Fig.  2. 

the  effect  of  displacing  an  atom  of  hydrogen  in  sulphuric  acid. 
Curves  for  K2S04  and  KH2P04  are  not  shown,  as  they  nearly 
coincide  with  2 KOH  and  H3P04  respectively. 

Discussion  of  Results. 

The  viscosity  of  sodium  salts  is  invariably  greater  than  that  of 
the  potassium  salts,  and  both  are  greater  than  that  of  the  corre- 
sponding acids.  The  effect  of  the  hypothetical  displacement  of  the 
first  atom  of  hydrogen  by  a given  base  is  generally  not  so  marked 
as  the  second  displacement  by  the  same  base.  NaHC4H406  is 
an  exception.  The  effect  of  the  second  atom  of  Na  and  K in  the 
phosphoric  acid  group  (see  Fig.  4)  is  very  marked.  Whether 


330 


B.  E.  MOORE. 


[VOL.  III. 

the  difference  is  due  to  the  position  of  the  hydrogen  atom  in  the 
molecule  is  a question,  perhaps,  easier  to  raise  than  to  answer 


1.6 

1.5 

1.4 

1.3 

1.2 

1.1 

V 


satisfactorily.  Coincident  with  the  entrance  of  the  second  atom 
of  Na  or  K is  the  change  from  marked  acid  to  basic  character, 

which  also  suggests  that  the  first 
change  in  H3P04  (=  H — P02 
— OH  — OH)  took  place  in  the 
hydroxide  radical,  the  second  in 
the  acid  radical,  and  the  third 
again  in  the  hydroxide  radical. 
The  curve  for  KH2P04  lies  too 
near  H3P04  to  be  credited  exten- 
sively. More  confidence  is  to  be 
placed  in  the  results  for  H3P04 
than  KH2P04,  as  Slotte’s  observa- 
tions for  H3P04  fall  practically 
upon  the  curve  here  given  for 
that  acid.  Again  the  neutral  phos- 
phate Na3P04  breaks  up  very 
easily  in  the  presence  of  H20  into 
the  ordinary  phosphate  Na2HP04  and  NaOH,  which  would  make 
one  accept  the  viscosity  curve  Na3P04  with  some  hesitation.  So 
that  on  the  whole  it  would  be  rather  difficult  to  draw  conclusions 


0.25  0.50  0.75  .1.  m. 


Fig.  4. 


0.25  0.50  0.75  1.  m.  1.25  1.50  1.75  2.;m. 


Fig.  3. 


I 


No.  5.] 


VISCOSITY  OF  SALT  SOLUTIONS. 


33* 


concerning  changes  in  the  radicals  from  the  viscosities.  So  much 
difficulty  does  not  present  itself  with  the  organic  compounds. 
The  addition  of  (CH2)2  to  C2H204  (=COOH  — COOH)  (see  Fig. 
5,  curves),  giving  COOH -CH2  — CH2- COOH,  increases  the  vis- 


Fig.  5. 


cosity  over  three  times  as  much  as  the  substitution  of  potassium  for 
hydrogen  in  (COOH)2.  The  farther  substitution  of  two  hydroxyl 
radicals  for  two  atoms  of  H in  (CH2)2  gives  also  a marked 
increase,  and  also  greater  than  % the  effect  of  potassium  substi- 


332 


B.  E.  MOORE. 


[Vol.  III. 


tuted  in  H2C204.  Again,  a comparison  of  curves  for  H2C204 
and  K2C204  with  the  curves  for  C4H604  and  K2C4H4Oe  shows 
a marked  difference  in  the  effects  of  potassium  on  the  two  salts. 
In  the  first  pair  of  solutions  potassium  entered  the  carboxyl,, 
giving  COOK  — COOK,  while  in  the  second  group  the  element 
potassium  has  worked  upon  the  hydroxide,  yielding  COOH  — 
CHOK-CHOK-COOH. 

A rrhenins  Exponential  Formula. 

When  Arrhenius  announced  the  exponential  formula,  r\  — Axr 
he  only  tested  it  to  1.5  gram-molecule  solutions.  Wagner,  who- 
validified  the  law  for  so  many  solutions,  did  not  go  above  the 
normal  solution.  So  that  it  was  thought  well  to  see  if  such  a 
formula  would  hold  for  more  concentrated  solutions.  To  test 
the  validity  of  the  law  for  very  dilute  solutions,  where  the  law  is 
most  serviceable,  it  would  be  necessary  to  limit  oneself  to  very 
narrow  range  of  and  small  changes  in  temperature.  It  would 
be  imperative  to  use  a bulb  A (Fig.  1)  of  smaller  volume  and  a 
capillary  d (Fig.  1)  of  very  small  bore.  The  latter  invariably 
clogs  and  prevents  accurate  results.  Even  such  precautions 
would,  at  the  best,  only  give  very  small  differences,  and  failure 
to  observe  these  precautions  could  not  account  for  the  variations 
from  the  logarithmic  law  observed  in  these  experiments.  The 
logarithmic  curve,  which  would  represent  the  viscosities  of  the 
more  dilute  solutions  of  NaOH,  e.g.  would,  if  extended  to  4 
and  8 molecule  solutions,  give  values  36  per  cent  and  75  per 
cent  too  small  respectively.  No  other  solutions  show  so  great 
a divergence.  Yet  in  the  double  normal  solutions  the  agreement 
is  rarely  better  than  3 per  cent  to  5 per  cent. 


Conductivities  and  Viscosities. 

The  values  for  A in  the  following  table  have  been  taken  direct 
from  the  tables  of  observations  on  y,  except  in  the  phosphoric 
acid  group,  where  A is  reckoned  from  the  equation  y = Ax  and 
x — m = J.  The  conductivities  K are  those  of  the  normal  solu- 
tions except  when  otherwise  noted.  Only  those  salts  are  given 


No.  5.] 


VISCOSITY  OF  SALT  SOLUTIONS . 


333 


for  which  the  conductivities  could  be  learned.  They  are  divided 
in  four  groups  corresponding  to  Tables  I.,  II.,  III.,  and  IV.  of 
Viscosities  respectively. 


Table  V. 


Substances. 

- 

A 

109  • K 

iNa2C03 

1.274 

42.7 

|NaHC03 

1.121 

37.9 

|K2C03  ...... 

1.138 

66.2 

1KHC03  ...... 

1.065 

61.3 

NaOH 

1.234 

149.0 

KOH 

1.11 

171.8 

fNa2S04 

— 

47.5 

2 NaHS04 

1.10 

— 

f K2S04 

1.106 

67.2 

\ khso4 

1.075 

173.6 

iNa3P04 

1.305 

97. 5 1 

iNa2HP04 

1.260 

79.6  j- 

3X2  normal  solution. 

\ NaH2P04 

1.105 

69.8) 

|H3P04 

1.08 

20.0 

|C4H606  

1.160 

46.04 

1 

\ c4h6o4 

1.110 

16.03 

V Yg  normal. 

fC2H204  

1.070 

26.7 

J 

|K2C204  

1.100 

68.8 

That,  while  the  viscosities  in  general  decrease,  the  conductivities 
of  a series  of  salts  increase,  as  noted  in  the  early  part  of  this  article, 
cannot  be  concluded  at  all  from  these  salts.  This  action  is  notice- 
able, however,  in  passing  from  the  sodium  salt  to  the  potassium  in 
the  first  and  second  group,  but  when  one  passes  either  from  sodium 
carbonate  or  from  potassium  carbonate  to  the  acid  salts,  viscosities 
and  conductivities  increase  and  decrease  together.  The  sulphates 
behave  in  the  same  manner.  In  the  third  or  phosphate  group,  in 
passing  from  Na3P04  to  H3P04,  both  viscosities  and  conductivities 
decrease.  In  the  fourth  or  organic  group,  there  is  an  irregularity 
in  the  conductivity  column.  This  list,  though  small,  is  enough  to 
show  that  there  is  little  hope  for  a successful  comparison  of  vis- 
cosity and  conductivity,  without  an  extended  series  of  observations, 


334 


B.  E.  MOORE. 


[Vol.  III. 


and  that,  too,  with  dilute  solutions  in  which  the  increase  in  the 
viscosity  of  the  solvent  will  be  largely  due  to  the  ions,  as  it  is 
the  viscosity  of  the  latter  alone  with  which  we  have  to  deal  in 
conductivity. 

Conclusions. 

1.  The  viscosity  of  solutions  decreases  quite  rapidly  with  rise  in 
temperature,  but  the  character  of  this  decrease  is  very  different 
for  different  concentrations  and  for  different  salt  solutions.1 

2.  Stochiometrical  relations,  though  doubtless  existing,  are 
neither  very  definite  nor  convincing. 

3.  The  Arrhenius  exponential  formula  or  law,  though  affording 
an  excellent  method  for  comparison  of  viscosities  of  dilute,  even 
normal,  solutions,  does  not  hold  good  for  the  more  concentrated 
solutions. 

4.  More  extended  observations  must  be  made  upon  the  relation 
of  viscosity  to  conductivity,  perhaps  even  some  new  method  of 
comparison  arrived  at,  before  the  two  subjects  are  placed  in  their 
right  relation. 

1 Thorpe  and  Rodgers,  Proc.  Royal  Soc.,  55,  p.  148,  have  pointed  out  that  tempera- 
tures of  equal  slopes  is  an  excellent  method  for  comparison  of  viscosity.  These  experi- 
ments were  in  a measure  completed  when  the  article  by  Thorpe  and  Rodgers  appeared, 
and  the  range  of  temperature  not  wide  enough  to  make  such  a comparison. 


